Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Complex Order Fractional Derivatives and Systems Are Non Hermitian

Version 1 : Received: 11 March 2021 / Approved: 15 March 2021 / Online: 15 March 2021 (16:23:56 CET)

How to cite: Ortigueira, M. The Complex Order Fractional Derivatives and Systems Are Non Hermitian. Preprints 2021, 2021030399 (doi: 10.20944/preprints202103.0399.v1). Ortigueira, M. The Complex Order Fractional Derivatives and Systems Are Non Hermitian. Preprints 2021, 2021030399 (doi: 10.20944/preprints202103.0399.v1).

Abstract

This paper discusses the concept of fractional derivative with complex order from the application point of view. It is shown that a fractional derivative is hermitian, if and only if the order is real. The hermitian part of complex order derivatives behave like allpass filters with almost logarithmic phase.

Subject Areas

Fractional derivative; Derivative order; Hermitian system; Complex order; Liouville derivative

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